Preheat your oven to 350 degrees F and prepare a muffin pan by placing liners inside or greasing with nonstick cooking spray.
Begin by cutting the peeled carrots into large chunks and place them in the bowl of a food processor or blender. Chop the carrots into small bits and set aside.
Next, in a large bowl, add the white sugar, brown sugar, applesauce, and eggs. Mix until well combined.
Fold in the chopped carrots.
In a separate bowl, whisk together the whole wheat flour, baking soda, baking powder, cinnamon, and salt.
Now combine the dry ingredients and wet ingredients, stirring until just incorporated.
Using an ice cream scoop or spoon, fill each muffin cup 2/3 of the way full with batter.
Bake for 20 to 25 minutes for full-sized muffins or 15 to 20 minutes for mini muffins. Muffins will be done when a toothpick inserted into the center comes out clean.
Allow muffins to cool in the pan for 10 minutes, then remove them to a wire cooling rack to cool completely before serving.